Stable evaluation of differential operators and linear and nonlinear multi-scale filtering.

Scherzer, Otmar

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Enhanced electrical impedance tomography via the Mumford–Shah functional

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We consider the problem of electrical impedance tomography where conductivity distribution in a domain is to be reconstructed from boundary measurements of voltage and currents. It is well-known that this problem is highly illposed. In this work, we propose the use of the Mumford–Shah functional, developed for segmentation and denoising of images, as a regularization. After establishing existence properties of the resulting variational problem, we proceed by demonstrating the approach...